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Minimizing properties of arbitrary solutions to the Ginzburg–Landau equation

Published online by Cambridge University Press:  14 November 2011

M. Comte  and
P. Mironescu
M. Comte
Affiliation:
Laboratoire d'Analyse Numérique, Tour 55–65, Université Pierre et Marie Curie, 4 place Jussieu, 75252 Paris Cedex 05, France
P. Mironescu
Affiliation:
Analyse Numérique et EDP, Université Paris Sud, Bâtiment 425, 91405 Orsay Cedex, France
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Extract

We consider the Ginzburg–Landau type equation

where G is a smooth bounded domain in ℝ2, g ∊ C∞(∂G;ℝ2 / {0}), and ε > 0 is a small parameter. We prove the uniqueness of solutions to this equation under some non-vanishing assumptions on uε, or under conditions on the boundary function g.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 129 , Issue 6 , 1999 , pp. 1157 - 1169
Copyright
Copyright © Royal Society of Edinburgh 1999

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